Understanding the Shirt Purchase Problem with Coupons

The problem asks us to find the lowest price Raghav has to pay for three shirts by choosing the better of two available discount coupons. We are given the individual prices of the three shirts and the conditions for using each coupon.

The prices of the three shirts are:

• Shirt 1: Rs. 1,250
• Shirt 2: Rs. 1,540
• Shirt 3: Rs. 1,375

Raghav buys all three shirts, which satisfies the minimum purchase condition for the second coupon.

Calculating Total Price Without Discount

First, let's find the total price of the three shirts without any discount:

Total Price = Price of Shirt 1 + Price of Shirt 2 + Price of Shirt 3

\( \text{Total Price} = 1250 + 1540 + 1375 \)

\( \text{Total Price} = 4165 \)

So, the total price of the three shirts is Rs. 4,165.

Analyzing Coupon Options and Calculating Costs

Option 1: Using the First Coupon (30% Total Discount)

The first coupon offers a flat 30% discount on the total amount. The total amount is Rs. 4,165.

Discount Amount = 30% of Total Price

\( \text{Discount Amount} = \frac{30}{100} \times 4165 \)

\( \text{Discount Amount} = 0.30 \times 4165 \)

\( \text{Discount Amount} = 1249.50 \)

Price with First Coupon = Total Price - Discount Amount

\( \text{Price with First Coupon} = 4165 - 1249.50 \)

\( \text{Price with First Coupon} = 2915.50 \)

So, the price after using the first coupon is Rs. 2,915.50.

Option 2: Using the Second Coupon (80% off Costliest Shirt)

The second coupon offers 80% off on the price of the costliest shirt, provided at least 3 shirts are purchased (which is the case here).

First, identify the costliest shirt among Rs. 1,250, Rs. 1,540, and Rs. 1,375.

The prices in ascending order are: Rs. 1,250, Rs. 1,375, Rs. 1,540.

The costliest shirt is the one priced at Rs. 1,540.

The discount is 80% on the price of this costliest shirt.

Discount on Costliest Shirt = 80% of Rs. 1,540

\( \text{Discount} = \frac{80}{100} \times 1540 \)

\( \text{Discount} = 0.80 \times 1540 \)

\( \text{Discount} = 1232 \)

The price of the costliest shirt after applying the discount will be:

Discounted Price of Costliest Shirt = Original Price - Discount

\( \text{Discounted Price} = 1540 - 1232 \)

\( \text{Discounted Price} = 308 \)

Alternatively, the discounted price is 20% of the original price (100% - 80% = 20%).

\( \text{Discounted Price} = \frac{20}{100} \times 1540 \)

\( \text{Discounted Price} = 0.20 \times 1540 \)

\( \text{Discounted Price} = 308 \)

The price with the second coupon is the sum of the full prices of the other two shirts plus the discounted price of the costliest shirt.

Price with Second Coupon = Price of Shirt 1 + Price of Shirt 3 + Discounted Price of Shirt 2

\( \text{Price with Second Coupon} = 1250 + 1375 + 308 \)

\( \text{Price with Second Coupon} = 2625 + 308 \)

\( \text{Price with Second Coupon} = 2933 \)

So, the price after using the second coupon is Rs. 2,933.

Determining the Minimum Price

Raghav can only use one coupon. We need to compare the prices obtained using each coupon to find the minimum price.

• Price with First Coupon: Rs. 2,915.50
• Price with Second Coupon: Rs. 2,933

Comparing the two prices, Rs. 2,915.50 is less than Rs. 2,933.

Therefore, the minimum price at which Raghav can purchase the three shirts is Rs. 2,915.50, using the first coupon.

Revision Table: Summary of Calculations

Comparing the final prices, the minimum price is Rs. 2,915.50.

Additional Information on Discounts and Percentages

Understanding discounts and percentages is crucial in shopping scenarios. A discount is a reduction in the original price of a product or service.

• Percentage Discount: This is a common way to represent a discount, indicating the fraction of the original price that is reduced. For example, a 30% discount means 30 out of every 100 units of currency from the price is deducted.
• Calculating Discount Amount: To find the discount amount, multiply the original price by the discount percentage (converted to a decimal).
  \( \text{Discount Amount} = \text{Original Price} \times \frac{\text{Discount Percentage}}{100} \)
• Calculating Final Price: To find the final price after a discount, subtract the discount amount from the original price.
  \( \text{Final Price} = \text{Original Price} - \text{Discount Amount} \)
  Alternatively, if the discount is D%, the final price is (100-D)% of the original price.
  \( \text{Final Price} = \text{Original Price} \times \frac{(100 - \text{Discount Percentage})}{100} \)
• Identifying Costliest Item: When a discount applies to a specific item like the "costliest shirt," you first need to compare the prices of all items being purchased to find the highest price.
• Comparing Offers: Often, stores provide multiple discount options or coupons. To get the best deal, you must calculate the final cost under each valid option and choose the one that results in the lowest total price. This problem demonstrates exactly this scenario.